CIE A Level Maths: Mechanics复习笔记2.3.2 suvat in 1D

What are the suvat (constant acceleration) formulae?

• For constant acceleration there are five suvat formula:

How do I identify values for suvat within a question?

•  Common phrases for displacement:
  • "…returns to its starting position …" is a way of saying s = 0
• Common phrases for velocity:
  • “… initially at rest …”, “… stationary …” are ways of saying u = 0
  • “… comes to rest …” is a way of saying v = 0
• Common phrases for acceleration:
  • “… falls freely …” is a way of saying a = ± g (see the gravity section)
• Sometimes you will need to use other techniques (such as Newton's Laws of Motion) to find the acceleration

How do I solve problems involving suvat?

• Step 1: Sketch (or add to) a diagram
  • Use key information in the question to include all relevant values
  • Make sure you clearly show which direction you are choosing to be positive
    • Choose the positive direction wisely, try to choose the direction which will result in fewer negative values needed
    • You could choose the initial direction of motion to be positive or you could choose the direction of acceleration to be positive.
• Step 2: Write down what you know and what you are trying to find
  • You should know 3 of the variables and need to find a 4th
  • It’s a good idea to go through each of the letters in the word suvat and make a note of the ones you know and which one you are trying to find
• Step 3: Select the appropriate equation(s)
• Step 4: Solve the equation(s) and problem
  • Include units in your answer and give your answer in context if appropriate

Can I use the suvat formulae for vertical motion?

• The suvat equations also apply to vertical motion (provided the acceleration is constant)
  • The positive direction is particularly important
• Acceleration will often be related to gravity

What can harder suvat problems look like?

• Some problems involve splitting the motion into more than one part
  • For example if acceleration has changed (but is constant for each part)
  • A key feature of these problems is that v (final velocity) for the first part of the motion will be u (initial velocity) for the second part of the motion
• Some problems do not appear to give you enough information
  • You may have to form two equations using the suvat formulae and solve them simultaneously
  • There may be more than one particle or multiple stages to the motion

(a)  Find the speed at the instant that the brakes are applied.

(b)  Find the deceleration of the car after the brakes have been applied.